Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\le n\le 7$

We prove optimal dispersive estimates for the wave group $e^{it\sqrt{-Δ+V}}$ for a class of real-valued potentials $V\in C^{(n-3)/2}({\bf R}^n)$, $4\le n\le 7$, such that $\partial_x^αV(x)=O(|x|^{-δ})$ for $|x|>1$, where $δ>(n+1)/2$.

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